We focus on low-lying level structure such as ΛΛN spin-spin and spin-orbit splittings in excitation spectra of p-sd shell Lambda hypernuclei. One of the major goals of hypernuclear physics is to understand properties of the baryon-baryon interaction including hyperon(s). Another important issue is to clarify dynamics of baryon many-body systems. In the last decades, by the developments of the experimental studies, the low-lying level structure of light ΛΛ hypernuclei has been revealed precisely. It is expected that crucial information on both properties of ΛΛN interaction and hypernuclear structure from the low-lying level structure. In this study, we use the antisymmetrized molecular dynamics with the ΛΛN G-matrix interaction derived from the baryon-baryon interaction model ESC. It is found that the ground-state spin-parity is systematically reproduced in the p-shell ΛΛ hypernuclei by tuning the ΛΛN spin-spin and spin-orbit interactions so as to reproduce the experimental data of 4ΛΛ4H, 7ΛΛ7Li, and 9ΛΛ9Be. Furthermore, it is found that the energy spacing of the ground-state doublet in 19ΛΛ19F is successfully reproduced using the same ΛΛN interaction. We also focus on the excitation energies and energy shifts of the excited doublets by the addition of a ΛΛ particle. In this talk, we will discuss how the spin-dependent properties of the ΛΛN interactions and structure of the core nuclei affect the low-lying spectra of the ΛΛ hypernucle